1. Field of the Invention
The invention relates to marketing of products and, more particularly, to arrangements for estimating product distribution and sales.
2. Background of the Invention
Manufacturers and distributors of retail products generally monitor product sales in order to maintain proper inventory and to direct marketing efforts. Monitoring may be done by sampling sales at retail outlets and transferring sales data to a central point for evaluation. Retail outlets usually cooperate in providing sales data but a significant number of retail outlets are not able to or do not elect to have sales data sampled in a form needed for analysis. As a result, it is necessary to estimate product sales of unsampled and poorly sampled individual outlets to provide marketing information.
In some industries, distribution of certain products is controlled so that additional data relating to the control of such products is needed for marketing purposes. In the pharmaceutical industry, for example, many products are sold by prescription and such sales are controlled by prescribing physicians. As a result, it is desirable to determine the number of prescriptions written by a physician so that marketing efforts may be directed at the prescribing physicians.
Estimates of business sales in small areas such as counties of a state have been made on the basis of known data for the state under the assumption that the relationships for the state also hold for the county. The article "Small-Area Estimation of Economic Statistics" by Cary T. Isaki, Journal of Business and Economic Statistics, Vol. D, No. 4, Oct. 1990, pages 435-441 describes a ratio correlation (multiple regression) approach for estimating retail sales for small areas (counties) using county-to-state shares of retail sales from two successive economic censuses. While these methods provide estimates of retail sales over a relatively small county area from publicly available data, they are not adapted to estimate retail sales of individual outlets where individual outlet characteristics differ widely. As a result, the estimates for individual outlets based on wide area data are biased and may not reflect actual sales of an individual outlet.
Estimation of physician prescribing activity has been attempted by marketing research practitioners based on ratio estimators and inflation factor estimators as commonly described in such texts as "Sampling Techniques" by W. G. Cochran, John Wiley, New York 1977. These methods attempt to estimate the activity in a pre-established geographic area of known dimensions by scaling up a sample of activity within the area in proportion to the level of a known auxiliary variable (i.e., ratio estimate) or in proportion to the level of sample coverage (via an inflation factor) for the entire area. Typical geographic areas encompass a plurality of outlets and prescribers. Such geographic-based methods do not yield estimates of each individual prescriber's activity within each individual outlet but only produce a measure of the total activity for the geography. If prescriber level estimates are desired, these methods must assume that the proportion of the total activity that is captured in the sample data (i.e., the captured proportion) of each prescriber is the same. If outlet estimates are desired, it must then be assumed that each unsampled outlet is accurately represented by the average of the sampled outlets in the geography. With these assumptions, all sample data within a stratum receive the same "scale-up" factor. These assumptions, however, are known to be false and result in biased estimates at the activity source level.
It is well known in the fields of resource exploration and mining to estimate data at locations which are not sampled and for which data is unavailable using data acquired at sampled locations by spatial correlation according to known physical principles. Stanley W. Zison U.S. Pat. No. 5,063,519 issued Nov. 5, 1991, for example, describes a method for estimating landfill gas production by measuring gas pressure in a soil cover at randomly selected locations in the landfill. A contour estimation of flow is generated and a prediction of the continuous spatial distribution of the landfill gas is produced.
John L. Spiesberger U.S. Pat. No. 4,995,011 issued Feb. 19, 1991 describes an acoustic mapping system in which the positions of acoustic transmitters is determined by processing data from five or more receivers distributed in a marine or terrestrial environment. The processing includes cross correlation of the receiver data and provides displays of computer generated maps.
Philip M. Doyen U.S. Pat. No. 4,926,394 issued May 15, 1990 discloses a Monte Carlo method for estimating lithography from seismic data in which discrete geological measurements of rock properties are combined with continuous measurements of seismic attributes. The combined measurements are converted into a display of the best estimate of subsurface rock classes.
The aforementioned patents are directed to spatially continuous processes in which estimation is done either by interpolating continuous spatial processes from data at known locations or by Monte Carlo simulations using the known data to determine an optimized estimate. In each process, reliance is placed on the laws of the underlying continuous physical process. It would be desirable to use spatial correlation to provide estimates of retail sales. Sales outlets such as pharmacies, however, do not form a group to which a common physical process applies but each outlet is a separate discrete entity with its own characteristics. Consequently, there is no underlying continuous physical process on which to base such correlation as in the aforementioned patents.